He established his reputation in Paris, particularly as a player of blindfold games. He lost a match in England to Howard Staunton in 1846 and drew a match with Adolf Anderssen in Germany in 1848.He lived in England from 1849 and founded the British Chess Review.In 1856 he moved to Paris where he won a match against de Riviere.In 1858 he played a match against Paul Morphy in Paris. Harrwitz won the first two games, but lost the match 5.5-2.5. Harrwitz withdrew from the match, allegedly on grounds of ill health.He subsequently retired to the Austrian Tyrol, dying there in 1884.

Harrwitz had a plus record against Anderssen. Although he had a negative record against Morphy, he was one of a few masters who beat Morphy with black pieces. Here is one of his wins in Paris in 1858 (moves given in Algebraic chess notation):